Pseudopotentials that move: From inertia to electromagnetism

Recent works have pointed out some worrisome inconsistencies in linear-response calculations performed with nonlocal pseudopotentials. Here we show that most of these issues are fixed by correctly adapting the pseudopotential to the motion of the corresponding nucleus, with a velocity dependence of the nonlocal operator. This prescription restores the correct Galilean covariance of the Schr"odinger equation, and the expected identity between mechanical rototranslations and electromagnetic perturbations. We demonstrate our arguments by relating the interatomic force constants to the electromagnetic susceptibility of the system via a set of exact sum rules. Among other virtues, these results conclusively reconcile the inertial and electrical definitions of the Drude weight in metals.